Why would they need to have LA? Or do you mean that it's not playable, RAW, w/o an LA listing? Awakened animals aren't that desirable from a power standpoint, IMO. However an awakened animal gains 2HD, and the lowest HD for large size is 3 (in the SRD). Does the HD gained from the Awaken Spell count as advancing the animal? If so, you could get away with awakening a hyena or a wolf at 4HD.